Santiago Canales

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The problem of minimizing the number of vertex-guards necessary to cover a given simple polygon (MINIMUM VERTEX GUARD (MVG) problem) is NP-hard. This computational complexity opens two lines of investigation: the development of algorithms that establish approximate solutions and the determination of optimal solutions for special classes of simple polygons.(More)
This paper discusses a distance guarding concept on triangulation graphs, which can be associated with distance domination and distance vertex cover. We show how these subjects are interconnected and provide tight bounds for any n-vertex maximal outerplanar graph: the 2d-guarding number, g2d(n) = ⌊ n 5 ⌋; the 2d-distance domination number, γ2d(n) = ⌊ n 5 ⌋;(More)
In this paper we focus on approximate solutions to solve a new class of Art Gallery Problems inspired by wireless localization. Instead of the usual guards we consider wireless devices whose signal can cross a certain number, k, of walls. These devices are called k-transmitters. We propose an algorithm for constructing the visibility region of a(More)
It is known that the maximum hidden vertex set problem on a given simple polygon is NP-hard (Shermer, 1989), therefore we focused on the development of approximation algorithms to tackle it. We propose four strategies to solve this problem, the first two (based on greedy constructive search) are designed specifically to solve it, and the other two are based(More)
We address the problem of stationing guards in vertices of a simple polygon in such a way that the whole polygon is guarded and the number of guards is minimum. This problem is NP-hard with relevant practical applications. In this paper we propose three metaheuristic approaches to this problem. Combined with the genetic algorithms strategy, which was(More)
This paper focuses on a variation of the Art Gallery problem that considers open edge guards and open mobile guards. A mobile guard can be placed on edges and diagonals of a polygon, and the “open” prefix means that the endpoints of such edge or diagonal are not taken into account for visibility purposes. This paper studies the number of guards that are(More)
In this paper we study some problems related to grid n-ogons. A grid n-ogon is a n-vertex orthogonal simple polygon, with no collinear edges, that may be placed in a (n 2 ) × (n 2 ) square grid. We will present some problems and results related to a subclass of grid n-ogons, the Thin grid n-ogons, in particular a classification for theses subclass of(More)